求数列1+1,1/2+4,1/4+7,...1/2的n-1次方+3n-2,前n项和Sn
问题描述:
求数列1+1,1/2+4,1/4+7,...1/2的n-1次方+3n-2,前n项和Sn
答
Sn=[1+4+7+……+(3n-2)]+(1+1/2+1/4+……+(1/2)^n-1)
=(1+3n-2)*n/2+[1-(1/2)^n]/(1-1/2)
=(3n-1)*n/2-2-2*(1/2)^n